Traditionally, in the theory of the Riemann Zeta function [1]}, the Euler-Maclaurin formula is used for the generalized summation of the Dirichlet series
\(\sum _{a<x}^b \phi (x)=\int _{a}^{b} \phi (x)dx+\int _{a}^{b}(x-[x]-\frac{1}{2}) \phi ^{\prime }(x)dx+(a-[a]-\frac{1}{2}) \phi (a)-(b-[b]-\frac{1}{2}) \phi (b);\) 
